Abstract
For the damped linear oscillator in Hilbert space X: x ̈ + B x ̇ + Ax = 0, A > 0, B ⩾ 0 , there can be no uniform decay rate if B is compact while the unit ball in X is not. The present paper uses control-theoretic methods to establish, in certain cases, explicit nonuniform decay rates. Examples of application to problems of stabilization and to problems concerning mixed, frictionally coupled elastic systems are studied in detail.
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